From ebc0e75c6cbcee78b0319b4c47a2597245a2303a Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Fri, 14 May 2021 12:51:04 +1200
Subject: [PATCH 01/14] Add error checks for set dimensions

---
 src/Bridges/Constraint/geomean.jl |   4 -
 src/sets.jl                       | 204 +++++++++++++++++++++++++++++-
 test/sets.jl                      |  27 +++-
 3 files changed, 226 insertions(+), 9 deletions(-)

diff --git a/src/Bridges/Constraint/geomean.jl b/src/Bridges/Constraint/geomean.jl
index 47f35d4d97..ce27a86124 100644
--- a/src/Bridges/Constraint/geomean.jl
+++ b/src/Bridges/Constraint/geomean.jl
@@ -64,10 +64,6 @@ function bridge_constraint(
     s::MOI.GeometricMeanCone,
 ) where {T,F,G,H}
     d = s.dimension
-    if d <= 1
-        # TODO change to a standard error: https://github.com/jump-dev/MathOptInterface.jl/issues/967
-        error("Dimension of GeometricMeanCone must be greater than 1.")
-    end
     n = d - 1
     l = ilog2(n)
     N = 1 << l
diff --git a/src/sets.jl b/src/sets.jl
index 26d1a0d386..8a0412fdce 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -112,6 +112,17 @@ The set ``\\mathbb{R}^{dimension}`` (containing all points) of dimension `dimens
 """
 struct Reals <: AbstractVectorSet
     dimension::Int
+    function Reals(dimension::Int)
+        if !(dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Dimension of Reals must be greater than 0, not " *
+                    "$(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::Reals) = Zeros(dimension(s))
@@ -124,6 +135,17 @@ The set ``\\{ 0 \\}^{dimension}`` (containing only the origin) of dimension `dim
 """
 struct Zeros <: AbstractVectorSet
     dimension::Int
+    function Zeros(dimension::Int)
+        if !(dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Dimension of Zeros must be greater than 0, not " *
+                    "$(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::Zeros) = Reals(dimension(s))
@@ -136,6 +158,17 @@ The nonnegative orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\ge 0 \\}`` of
 """
 struct Nonnegatives <: AbstractVectorSet
     dimension::Int
+    function Nonnegatives(dimension::Int)
+        if !(dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Dimension of Nonnegatives must be greater than 0, not " *
+                    "$(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::Nonnegatives) = copy(s)
@@ -148,6 +181,17 @@ The nonpositive orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\le 0 \\}`` of
 """
 struct Nonpositives <: AbstractVectorSet
     dimension::Int
+    function Nonpositives(dimension::Int)
+        if !(dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Dimension of Nonpositives must be greater than 0, not " *
+                    "$(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::Nonpositives) = copy(s)
@@ -230,6 +274,17 @@ The ``\\ell_\\infty``-norm cone ``\\{ (t,x) \\in \\mathbb{R}^{dimension} : t \\g
 """
 struct NormInfinityCone <: AbstractVectorSet
     dimension::Int
+    function NormInfinityCone(dimension::Int)
+        if !(dimension > 1)
+            throw(
+                DimensionMismatch(
+                    "Dimension of NormInfinityCone must be greater than 1, " *
+                    "not $(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::NormInfinityCone) = NormOneCone(dimension(s))
@@ -242,6 +297,17 @@ The ``\\ell_1``-norm cone ``\\{ (t,x) \\in \\mathbb{R}^{dimension} : t \\ge \\lV
 """
 struct NormOneCone <: AbstractVectorSet
     dimension::Int
+    function NormOneCone(dimension::Int)
+        if !(dimension > 1)
+            throw(
+                DimensionMismatch(
+                    "Dimension of NormOneCone must be greater than 1, not " *
+                    "$(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::NormOneCone) = NormInfinityCone(dimension(s))
@@ -254,6 +320,17 @@ The second-order cone (or Lorenz cone or ``\\ell_2``-norm cone) ``\\{ (t,x) \\in
 """
 struct SecondOrderCone <: AbstractVectorSet
     dimension::Int
+    function SecondOrderCone(dimension::Int)
+        if !(dimension > 1)
+            throw(
+                DimensionMismatch(
+                    "Dimension of SecondOrderCone must be greater than 1, " *
+                    "not $(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::SecondOrderCone) = copy(s)
@@ -266,6 +343,17 @@ The rotated second-order cone ``\\{ (t,u,x) \\in \\mathbb{R}^{dimension} : 2tu \
 """
 struct RotatedSecondOrderCone <: AbstractVectorSet
     dimension::Int
+    function RotatedSecondOrderCone(dimension::Int)
+        if !(dimension > 2)
+            throw(
+                DimensionMismatch(
+                    "Dimension of RotatedSecondOrderCone must be greater " *
+                    "than 2, not $(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 dual_set(s::RotatedSecondOrderCone) = copy(s)
@@ -283,6 +371,17 @@ The dual of the geometric mean cone is
 """
 struct GeometricMeanCone <: AbstractVectorSet
     dimension::Int
+    function GeometricMeanCone(dimension::Int)
+        if !(dimension > 1)
+            throw(
+                DimensionMismatch(
+                    "Dimension of GeometricMeanCone must be greater than 1, " *
+                    "not $(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 """
@@ -351,6 +450,17 @@ The dual of the relative entropy cone is
 """
 struct RelativeEntropyCone <: AbstractVectorSet
     dimension::Int
+    function RelativeEntropyCone(dimension::Int)
+        if !(dimension > 1 && isodd(dimension))
+            throw(
+                DimensionMismatch(
+                    "Dimension of RelativeEntropyCone must be greater an odd " *
+                    "integer greater than 2, not $(dimension).",
+                ),
+            )
+        end
+        return new(dimension)
+    end
 end
 
 """
@@ -362,6 +472,17 @@ The matrix X is vectorized by stacking the columns, matching the behavior of Jul
 struct NormSpectralCone <: AbstractVectorSet
     row_dim::Int
     column_dim::Int
+    function NormSpectralCone(row_dim::Int, column_dim::Int)
+        if !(row_dim > 0 && column_dim > 0)
+            throw(
+                DimensionMismatch(
+                    "Dimension of NormSpectralCone must be strictly " *
+                    "positive, not ($(row_dim), $(column_dim)).",
+                ),
+            )
+        end
+        return new(row_dim, column_dim)
+    end
 end
 
 dual_set(s::NormSpectralCone) = NormNuclearCone(s.row_dim, s.column_dim)
@@ -376,6 +497,17 @@ The matrix X is vectorized by stacking the columns, matching the behavior of Jul
 struct NormNuclearCone <: AbstractVectorSet
     row_dim::Int
     column_dim::Int
+    function NormNuclearCone(row_dim::Int, column_dim::Int)
+        if !(row_dim > 0 && column_dim > 0)
+            throw(
+                DimensionMismatch(
+                    "Dimension of NormNuclearCone must be strictly " *
+                    "positive, not ($(row_dim), $(column_dim)).",
+                ),
+            )
+        end
+        return new(row_dim, column_dim)
+    end
 end
 
 dual_set(s::NormNuclearCone) = NormSpectralCone(s.row_dim, s.column_dim)
@@ -560,6 +692,17 @@ form.
 """
 struct PositiveSemidefiniteConeTriangle <: AbstractSymmetricMatrixSetTriangle
     side_dimension::Int
+    function PositiveSemidefiniteConeTriangle(side_dimension::Int)
+        if !(side_dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Side dimension of PositiveSemidefiniteConeTriangle must " *
+                    "be strictly positive, not $(side_dimension).",
+                ),
+            )
+        end
+        return new(side_dimension)
+    end
 end
 
 dual_set(s::PositiveSemidefiniteConeTriangle) = copy(s)
@@ -593,6 +736,17 @@ It both constrains ``y = z`` and ``(1, -y, 0)`` (or ``(1, -z, 0)``) to be in `Po
 """
 struct PositiveSemidefiniteConeSquare <: AbstractSymmetricMatrixSetSquare
     side_dimension::Int
+    function PositiveSemidefiniteConeSquare(side_dimension::Int)
+        if !(side_dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Side dimension of PositiveSemidefiniteConeSquare must " *
+                    "be strictly positive, not $(side_dimension).",
+                ),
+            )
+        end
+        return new(side_dimension)
+    end
 end
 
 function _dual_set_square_error()
@@ -620,6 +774,17 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct LogDetConeTriangle <: AbstractVectorSet
     side_dimension::Int
+    function LogDetConeTriangle(side_dimension::Int)
+        if !(side_dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Side dimension of LogDetConeTriangle must " *
+                    "be strictly positive, not $(side_dimension).",
+                ),
+            )
+        end
+        return new(side_dimension)
+    end
 end
 
 function dimension(s::LogDetConeTriangle)
@@ -635,6 +800,17 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct LogDetConeSquare <: AbstractVectorSet
     side_dimension::Int
+    function LogDetConeSquare(side_dimension::Int)
+        if !(side_dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Side dimension of LogDetConeSquare must " *
+                    "be strictly positive, not $(side_dimension).",
+                ),
+            )
+        end
+        return new(side_dimension)
+    end
 end
 
 dimension(s::LogDetConeSquare) = 2 + s.side_dimension^2
@@ -647,6 +823,17 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct RootDetConeTriangle <: AbstractVectorSet
     side_dimension::Int
+    function RootDetConeTriangle(side_dimension::Int)
+        if !(side_dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Side dimension of RootDetConeTriangle must " *
+                    "be strictly positive, not $(side_dimension).",
+                ),
+            )
+        end
+        return new(side_dimension)
+    end
 end
 
 function dimension(s::RootDetConeTriangle)
@@ -662,6 +849,17 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct RootDetConeSquare <: AbstractVectorSet
     side_dimension::Int
+    function RootDetConeSquare(side_dimension::Int)
+        if !(side_dimension > 0)
+            throw(
+                DimensionMismatch(
+                    "Side dimension of RootDetConeSquare must " *
+                    "be strictly positive, not $(side_dimension).",
+                ),
+            )
+        end
+        return new(side_dimension)
+    end
 end
 
 dimension(s::RootDetConeSquare) = 1 + s.side_dimension^2
@@ -855,10 +1053,10 @@ struct Complements <: AbstractVectorSet
     # Need an explicit Int64 here, because JSON parses Int as Int64, even on
     # 32-bit machines.
     function Complements(dimension::Union{Int,Int64})
-        if !iseven(dimension)
+        if !(dimension > 0 && iseven(dimension))
             throw(
-                ArgumentError(
-                    "The dimension of a Complements set must be even.",
+                DimensionMismatch(
+                    "Dimension of Complements must be even, not $(dimension).",
                 ),
             )
         end
diff --git a/test/sets.jl b/test/sets.jl
index 829ee99797..52bd68d471 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -114,8 +114,31 @@ function test_sets_dimension()
     @test MOI.dimension(MOI.Complements(10)) == 10
 end
 
-function test_sets_complement()
-    @test_throws ArgumentError MOI.Complements(3)
+function test_sets_DimensionMismatch()
+    @test_throws DimensionMismatch MOI.Reals(0)
+    @test_throws DimensionMismatch MOI.Zeros(0)
+    @test_throws DimensionMismatch MOI.Nonnegatives(0)
+    @test_throws DimensionMismatch MOI.Nonpositives(0)
+    @test_throws DimensionMismatch MOI.NormInfinityCone(1)
+    @test_throws DimensionMismatch MOI.NormOneCone(1)
+    @test_throws DimensionMismatch MOI.SecondOrderCone(1)
+    @test_throws DimensionMismatch MOI.RotatedSecondOrderCone(2)
+    @test_throws DimensionMismatch MOI.GeometricMeanCone(1)
+    @test_throws DimensionMismatch MOI.RelativeEntropyCone(1)
+    @test_throws DimensionMismatch MOI.RelativeEntropyCone(4)
+    @test_throws DimensionMismatch MOI.NormSpectralCone(1, 0)
+    @test_throws DimensionMismatch MOI.NormSpectralCone(0, 1)
+    @test_throws DimensionMismatch MOI.NormNuclearCone(1, 0)
+    @test_throws DimensionMismatch MOI.NormNuclearCone(0, 1)
+    @test_throws DimensionMismatch MOI.PositiveSemidefiniteConeTriangle(0)
+    @test_throws DimensionMismatch MOI.PositiveSemidefiniteConeSquare(0)
+    @test_throws DimensionMismatch MOI.LogDetConeTriangle(0)
+    @test_throws DimensionMismatch MOI.LogDetConeSquare(0)
+    @test_throws DimensionMismatch MOI.RootDetConeTriangle(0)
+    @test_throws DimensionMismatch MOI.RootDetConeSquare(0)
+    @test_throws DimensionMismatch MOI.Complements(0)
+    @test_throws DimensionMismatch MOI.Complements(3)
+    return
 end
 
 function _dual_set_test(set1, set2)

From be15d9e086870e17ef612dd98efb68b82558aa41 Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Fri, 14 May 2021 13:20:17 +1200
Subject: [PATCH 02/14] Fix

---
 src/sets.jl  | 44 +++++++++++++++++++++-----------------------
 test/sets.jl |  6 +++---
 2 files changed, 24 insertions(+), 26 deletions(-)

diff --git a/src/sets.jl b/src/sets.jl
index 8a0412fdce..fc1143e97b 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -112,7 +112,7 @@ The set ``\\mathbb{R}^{dimension}`` (containing all points) of dimension `dimens
 """
 struct Reals <: AbstractVectorSet
     dimension::Int
-    function Reals(dimension::Int)
+    function Reals(dimension::Base.Integer)
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
@@ -135,7 +135,7 @@ The set ``\\{ 0 \\}^{dimension}`` (containing only the origin) of dimension `dim
 """
 struct Zeros <: AbstractVectorSet
     dimension::Int
-    function Zeros(dimension::Int)
+    function Zeros(dimension::Base.Integer)
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
@@ -158,7 +158,7 @@ The nonnegative orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\ge 0 \\}`` of
 """
 struct Nonnegatives <: AbstractVectorSet
     dimension::Int
-    function Nonnegatives(dimension::Int)
+    function Nonnegatives(dimension::Base.Integer)
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
@@ -181,7 +181,7 @@ The nonpositive orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\le 0 \\}`` of
 """
 struct Nonpositives <: AbstractVectorSet
     dimension::Int
-    function Nonpositives(dimension::Int)
+    function Nonpositives(dimension::Base.Integer)
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
@@ -274,7 +274,7 @@ The ``\\ell_\\infty``-norm cone ``\\{ (t,x) \\in \\mathbb{R}^{dimension} : t \\g
 """
 struct NormInfinityCone <: AbstractVectorSet
     dimension::Int
-    function NormInfinityCone(dimension::Int)
+    function NormInfinityCone(dimension::Base.Integer)
         if !(dimension > 1)
             throw(
                 DimensionMismatch(
@@ -297,7 +297,7 @@ The ``\\ell_1``-norm cone ``\\{ (t,x) \\in \\mathbb{R}^{dimension} : t \\ge \\lV
 """
 struct NormOneCone <: AbstractVectorSet
     dimension::Int
-    function NormOneCone(dimension::Int)
+    function NormOneCone(dimension::Base.Integer)
         if !(dimension > 1)
             throw(
                 DimensionMismatch(
@@ -320,7 +320,7 @@ The second-order cone (or Lorenz cone or ``\\ell_2``-norm cone) ``\\{ (t,x) \\in
 """
 struct SecondOrderCone <: AbstractVectorSet
     dimension::Int
-    function SecondOrderCone(dimension::Int)
+    function SecondOrderCone(dimension::Base.Integer)
         if !(dimension > 1)
             throw(
                 DimensionMismatch(
@@ -343,7 +343,7 @@ The rotated second-order cone ``\\{ (t,u,x) \\in \\mathbb{R}^{dimension} : 2tu \
 """
 struct RotatedSecondOrderCone <: AbstractVectorSet
     dimension::Int
-    function RotatedSecondOrderCone(dimension::Int)
+    function RotatedSecondOrderCone(dimension::Base.Integer)
         if !(dimension > 2)
             throw(
                 DimensionMismatch(
@@ -371,7 +371,7 @@ The dual of the geometric mean cone is
 """
 struct GeometricMeanCone <: AbstractVectorSet
     dimension::Int
-    function GeometricMeanCone(dimension::Int)
+    function GeometricMeanCone(dimension::Base.Integer)
         if !(dimension > 1)
             throw(
                 DimensionMismatch(
@@ -450,7 +450,7 @@ The dual of the relative entropy cone is
 """
 struct RelativeEntropyCone <: AbstractVectorSet
     dimension::Int
-    function RelativeEntropyCone(dimension::Int)
+    function RelativeEntropyCone(dimension::Base.Integer)
         if !(dimension > 1 && isodd(dimension))
             throw(
                 DimensionMismatch(
@@ -472,7 +472,7 @@ The matrix X is vectorized by stacking the columns, matching the behavior of Jul
 struct NormSpectralCone <: AbstractVectorSet
     row_dim::Int
     column_dim::Int
-    function NormSpectralCone(row_dim::Int, column_dim::Int)
+    function NormSpectralCone(row_dim::Base.Integer, column_dim::Base.Integer)
         if !(row_dim > 0 && column_dim > 0)
             throw(
                 DimensionMismatch(
@@ -497,7 +497,7 @@ The matrix X is vectorized by stacking the columns, matching the behavior of Jul
 struct NormNuclearCone <: AbstractVectorSet
     row_dim::Int
     column_dim::Int
-    function NormNuclearCone(row_dim::Int, column_dim::Int)
+    function NormNuclearCone(row_dim::Base.Integer, column_dim::Base.Integer)
         if !(row_dim > 0 && column_dim > 0)
             throw(
                 DimensionMismatch(
@@ -692,7 +692,7 @@ form.
 """
 struct PositiveSemidefiniteConeTriangle <: AbstractSymmetricMatrixSetTriangle
     side_dimension::Int
-    function PositiveSemidefiniteConeTriangle(side_dimension::Int)
+    function PositiveSemidefiniteConeTriangle(side_dimension::Base.Integer)
         if !(side_dimension > 0)
             throw(
                 DimensionMismatch(
@@ -736,7 +736,7 @@ It both constrains ``y = z`` and ``(1, -y, 0)`` (or ``(1, -z, 0)``) to be in `Po
 """
 struct PositiveSemidefiniteConeSquare <: AbstractSymmetricMatrixSetSquare
     side_dimension::Int
-    function PositiveSemidefiniteConeSquare(side_dimension::Int)
+    function PositiveSemidefiniteConeSquare(side_dimension::Base.Integer)
         if !(side_dimension > 0)
             throw(
                 DimensionMismatch(
@@ -774,7 +774,7 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct LogDetConeTriangle <: AbstractVectorSet
     side_dimension::Int
-    function LogDetConeTriangle(side_dimension::Int)
+    function LogDetConeTriangle(side_dimension::Base.Integer)
         if !(side_dimension > 0)
             throw(
                 DimensionMismatch(
@@ -800,7 +800,7 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct LogDetConeSquare <: AbstractVectorSet
     side_dimension::Int
-    function LogDetConeSquare(side_dimension::Int)
+    function LogDetConeSquare(side_dimension::Base.Integer)
         if !(side_dimension > 0)
             throw(
                 DimensionMismatch(
@@ -823,7 +823,7 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct RootDetConeTriangle <: AbstractVectorSet
     side_dimension::Int
-    function RootDetConeTriangle(side_dimension::Int)
+    function RootDetConeTriangle(side_dimension::Base.Integer)
         if !(side_dimension > 0)
             throw(
                 DimensionMismatch(
@@ -849,7 +849,7 @@ The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
 """
 struct RootDetConeSquare <: AbstractVectorSet
     side_dimension::Int
-    function RootDetConeSquare(side_dimension::Int)
+    function RootDetConeSquare(side_dimension::Base.Integer)
         if !(side_dimension > 0)
             throw(
                 DimensionMismatch(
@@ -997,7 +997,7 @@ function Base.:(==)(
 end
 
 """
-    Complements(dimension::Int)
+    Complements(dimension::Base.Integer)
 
 The set corresponding to a mixed complementarity constraint.
 
@@ -1050,9 +1050,7 @@ defines the complementarity problem where `0 <= x_1 ⟂ x_3 >= 0` and
 """
 struct Complements <: AbstractVectorSet
     dimension::Int
-    # Need an explicit Int64 here, because JSON parses Int as Int64, even on
-    # 32-bit machines.
-    function Complements(dimension::Union{Int,Int64})
+    function Complements(dimension::Base.Integer)
         if !(dimension > 0 && iseven(dimension))
             throw(
                 DimensionMismatch(
@@ -1060,7 +1058,7 @@ struct Complements <: AbstractVectorSet
                 ),
             )
         end
-        return new(convert(Int, dimension))
+        return new(dimension)
     end
 end
 
diff --git a/test/sets.jl b/test/sets.jl
index 52bd68d471..910e151a5f 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -205,10 +205,10 @@ function test_sets_dual_soc()
 end
 
 function test_sets_dual_rsoc()
-    rsoc2 = MOI.RotatedSecondOrderCone(2)
+    # rsoc2 = MOI.RotatedSecondOrderCone(2)
     rsoc3 = MOI.RotatedSecondOrderCone(3)
-    _self_dual_set_test(rsoc2)
-    @test MOI.dual_set(rsoc2) != rsoc3
+    # _self_dual_set_test(rsoc2)
+    # @test MOI.dual_set(rsoc2) != rsoc3
     _self_dual_set_test(rsoc3)
     return
 end

From b3817368d4300a539e6d86324f295262202f1d0a Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Fri, 14 May 2021 14:22:24 +1200
Subject: [PATCH 03/14] Fix Zeros(0)

---
 test/Bridges/Variable/map.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Bridges/Variable/map.jl b/test/Bridges/Variable/map.jl
index 6d5ab34aa4..b3bffd5cb9 100644
--- a/test/Bridges/Variable/map.jl
+++ b/test/Bridges/Variable/map.jl
@@ -87,7 +87,7 @@ v2, c2 = MOIB.Variable.add_keys_for_bridge(map, () -> b2, set2)
 end
 
 b3 = VariableDummyBridge(3)
-set3 = MOI.Zeros(0)
+set3 = MOI.Zeros(1)
 v3, c3 = MOIB.Variable.add_keys_for_bridge(map, () -> b3, set3)
 @testset "Vector set of length 0" begin
     @test isempty(v3)

From 563a9659477cb6860e0efa7eef56d124c25a8293 Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Mon, 17 May 2021 12:10:17 +1200
Subject: [PATCH 04/14] Reduce dimension of some cones

---
 src/sets.jl  | 23 +++++++++++------------
 test/sets.jl | 14 +++++++-------
 2 files changed, 18 insertions(+), 19 deletions(-)

diff --git a/src/sets.jl b/src/sets.jl
index fc1143e97b..5cb7d058e4 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -275,11 +275,11 @@ The ``\\ell_\\infty``-norm cone ``\\{ (t,x) \\in \\mathbb{R}^{dimension} : t \\g
 struct NormInfinityCone <: AbstractVectorSet
     dimension::Int
     function NormInfinityCone(dimension::Base.Integer)
-        if !(dimension > 1)
+        if !(dimension >= 1)
             throw(
                 DimensionMismatch(
-                    "Dimension of NormInfinityCone must be greater than 1, " *
-                    "not $(dimension).",
+                    "Dimension of NormInfinityCone must be >= 1, not" *
+                    "$(dimension).",
                 ),
             )
         end
@@ -298,11 +298,10 @@ The ``\\ell_1``-norm cone ``\\{ (t,x) \\in \\mathbb{R}^{dimension} : t \\ge \\lV
 struct NormOneCone <: AbstractVectorSet
     dimension::Int
     function NormOneCone(dimension::Base.Integer)
-        if !(dimension > 1)
+        if !(dimension >= 1)
             throw(
                 DimensionMismatch(
-                    "Dimension of NormOneCone must be greater than 1, not " *
-                    "$(dimension).",
+                    "Dimension of NormOneCone must be >= 1, not $(dimension).",
                 ),
             )
         end
@@ -321,11 +320,11 @@ The second-order cone (or Lorenz cone or ``\\ell_2``-norm cone) ``\\{ (t,x) \\in
 struct SecondOrderCone <: AbstractVectorSet
     dimension::Int
     function SecondOrderCone(dimension::Base.Integer)
-        if !(dimension > 1)
+        if !(dimension >= 1)
             throw(
                 DimensionMismatch(
-                    "Dimension of SecondOrderCone must be greater than 1, " *
-                    "not $(dimension).",
+                    "Dimension of SecondOrderCone must be >= 1, not " *
+                    "$(dimension).",
                 ),
             )
         end
@@ -344,11 +343,11 @@ The rotated second-order cone ``\\{ (t,u,x) \\in \\mathbb{R}^{dimension} : 2tu \
 struct RotatedSecondOrderCone <: AbstractVectorSet
     dimension::Int
     function RotatedSecondOrderCone(dimension::Base.Integer)
-        if !(dimension > 2)
+        if !(dimension >= 2)
             throw(
                 DimensionMismatch(
-                    "Dimension of RotatedSecondOrderCone must be greater " *
-                    "than 2, not $(dimension).",
+                    "Dimension of RotatedSecondOrderCone must be >= 2, not " *
+                    "$(dimension).",
                 ),
             )
         end
diff --git a/test/sets.jl b/test/sets.jl
index 910e151a5f..e98d3e697c 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -119,10 +119,10 @@ function test_sets_DimensionMismatch()
     @test_throws DimensionMismatch MOI.Zeros(0)
     @test_throws DimensionMismatch MOI.Nonnegatives(0)
     @test_throws DimensionMismatch MOI.Nonpositives(0)
-    @test_throws DimensionMismatch MOI.NormInfinityCone(1)
-    @test_throws DimensionMismatch MOI.NormOneCone(1)
-    @test_throws DimensionMismatch MOI.SecondOrderCone(1)
-    @test_throws DimensionMismatch MOI.RotatedSecondOrderCone(2)
+    @test_throws DimensionMismatch MOI.NormInfinityCone(0)
+    @test_throws DimensionMismatch MOI.NormOneCone(0)
+    @test_throws DimensionMismatch MOI.SecondOrderCone(0)
+    @test_throws DimensionMismatch MOI.RotatedSecondOrderCone(1)
     @test_throws DimensionMismatch MOI.GeometricMeanCone(1)
     @test_throws DimensionMismatch MOI.RelativeEntropyCone(1)
     @test_throws DimensionMismatch MOI.RelativeEntropyCone(4)
@@ -205,10 +205,10 @@ function test_sets_dual_soc()
 end
 
 function test_sets_dual_rsoc()
-    # rsoc2 = MOI.RotatedSecondOrderCone(2)
+    rsoc2 = MOI.RotatedSecondOrderCone(2)
     rsoc3 = MOI.RotatedSecondOrderCone(3)
-    # _self_dual_set_test(rsoc2)
-    # @test MOI.dual_set(rsoc2) != rsoc3
+    _self_dual_set_test(rsoc2)
+    @test MOI.dual_set(rsoc2) != rsoc3
     _self_dual_set_test(rsoc3)
     return
 end

From 38ed6b53a5169d91b7aff284f666a091d64ae852 Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Mon, 17 May 2021 12:12:58 +1200
Subject: [PATCH 05/14] Reword errors

---
 src/sets.jl | 22 +++++++++-------------
 1 file changed, 9 insertions(+), 13 deletions(-)

diff --git a/src/sets.jl b/src/sets.jl
index 5cb7d058e4..85a490c56b 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -116,8 +116,7 @@ struct Reals <: AbstractVectorSet
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Reals must be greater than 0, not " *
-                    "$(dimension).",
+                    "Dimension of Reals must be > 0, not $(dimension).",
                 ),
             )
         end
@@ -139,8 +138,7 @@ struct Zeros <: AbstractVectorSet
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Zeros must be greater than 0, not " *
-                    "$(dimension).",
+                    "Dimension of Zeros must be > 0, not $(dimension).",
                 ),
             )
         end
@@ -162,8 +160,7 @@ struct Nonnegatives <: AbstractVectorSet
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Nonnegatives must be greater than 0, not " *
-                    "$(dimension).",
+                    "Dimension of Nonnegatives must be > 0, not $(dimension).",
                 ),
             )
         end
@@ -185,8 +182,7 @@ struct Nonpositives <: AbstractVectorSet
         if !(dimension > 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Nonpositives must be greater than 0, not " *
-                    "$(dimension).",
+                    "Dimension of Nonpositives must be > 0, not $(dimension).",
                 ),
             )
         end
@@ -374,8 +370,8 @@ struct GeometricMeanCone <: AbstractVectorSet
         if !(dimension > 1)
             throw(
                 DimensionMismatch(
-                    "Dimension of GeometricMeanCone must be greater than 1, " *
-                    "not $(dimension).",
+                    "Dimension of GeometricMeanCone must be > 1, not " *
+                    "$(dimension).",
                 ),
             )
         end
@@ -450,11 +446,11 @@ The dual of the relative entropy cone is
 struct RelativeEntropyCone <: AbstractVectorSet
     dimension::Int
     function RelativeEntropyCone(dimension::Base.Integer)
-        if !(dimension > 1 && isodd(dimension))
+        if !(dimension >= 3 && isodd(dimension))
             throw(
                 DimensionMismatch(
-                    "Dimension of RelativeEntropyCone must be greater an odd " *
-                    "integer greater than 2, not $(dimension).",
+                    "Dimension of RelativeEntropyCone must be an odd integer " *
+                    ">= 3, not $(dimension).",
                 ),
             )
         end

From d6ff6df2ac0657a81c10b45c0a3752fe9b8ad05e Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Mon, 17 May 2021 13:58:26 +1200
Subject: [PATCH 06/14] Add ZeroDimSet

---
 test/Bridges/Variable/map.jl | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/test/Bridges/Variable/map.jl b/test/Bridges/Variable/map.jl
index b3bffd5cb9..bf3de204ef 100644
--- a/test/Bridges/Variable/map.jl
+++ b/test/Bridges/Variable/map.jl
@@ -86,13 +86,15 @@ v2, c2 = MOIB.Variable.add_keys_for_bridge(map, () -> b2, set2)
     @test collect(values(map)) == [b1, b2]
 end
 
+struct _ZeroDimSet <: MOI.AbstractVectorSet
+    dimension::Int
+end
 b3 = VariableDummyBridge(3)
-set3 = MOI.Zeros(1)
+set3 = _ZeroDimSet(0)
 v3, c3 = MOIB.Variable.add_keys_for_bridge(map, () -> b3, set3)
 @testset "Vector set of length 0" begin
     @test isempty(v3)
     @test c3.value == 0
-
     bridges = collect(values(map))
     @test sort([b.id for b in bridges]) == 1:2
     elements = sort(collect(map), by = el -> el.second.id)

From f38e422c53ffc24616182c4cc480da286ae8f464 Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Mon, 17 May 2021 14:41:45 +1200
Subject: [PATCH 07/14] Fix SDPA

---
 src/FileFormats/SDPA/SDPA.jl | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/src/FileFormats/SDPA/SDPA.jl b/src/FileFormats/SDPA/SDPA.jl
index 3c0aa540f8..079a538ec6 100644
--- a/src/FileFormats/SDPA/SDPA.jl
+++ b/src/FileFormats/SDPA/SDPA.jl
@@ -164,10 +164,12 @@ function Base.write(io::IO, model::Model{T}) where {T}
     end
     println(io)
 
-    index_map = Vector{Tuple{Int,Int}}(
-        undef,
-        MOI.dimension(MOI.PositiveSemidefiniteConeTriangle(max_dim)),
-    )
+    max_index_dim = if max_dim > 0
+        MOI.dimension(MOI.PositiveSemidefiniteConeTriangle(max_dim))
+    else
+        0
+    end
+    index_map = Vector{Tuple{Int,Int}}(undef, max_index_dim)
     k = 0
     for col in 1:max_dim
         for row in 1:col

From 40034b57a047651f236b5c7f7afe5a5f176e75cd Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Mon, 17 May 2021 15:19:13 +1200
Subject: [PATCH 08/14] Fix

---
 test/Utilities/model.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/test/Utilities/model.jl b/test/Utilities/model.jl
index 8af12b62c9..584d6c7de0 100644
--- a/test/Utilities/model.jl
+++ b/test/Utilities/model.jl
@@ -354,8 +354,8 @@ end
         }(),
     )
 
-    f5 = MOI.VectorOfVariables([x])
-    c5 = MOI.add_constraint(model, f5, MOI.RotatedSecondOrderCone(1))
+    f5 = MOI.VectorOfVariables([x, x])
+    c5 = MOI.add_constraint(model, f5, MOI.RotatedSecondOrderCone(2))
     @test 1 == @inferred MOI.get(
         model,
         MOI.NumberOfConstraints{

From 573be94bca312fdcd8a75b7758b0f0c213e7e089 Mon Sep 17 00:00:00 2001
From: odow <o.dowson@gmail.com>
Date: Mon, 7 Jun 2021 11:05:58 +1200
Subject: [PATCH 09/14] Allow empty sets

---
 src/sets.jl  | 190 ++++++++++++++++++++++++++++++++-------------------
 test/sets.jl |  53 ++++++++------
 2 files changed, 152 insertions(+), 91 deletions(-)

diff --git a/src/sets.jl b/src/sets.jl
index 85a490c56b..1c818858ce 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -108,15 +108,16 @@ dimension(s::AbstractVectorSet) = s.dimension # .dimension field is conventional
 """
     Reals(dimension)
 
-The set ``\\mathbb{R}^{dimension}`` (containing all points) of dimension `dimension`.
+The set ``\\mathbb{R}^{dimension}`` (containing all points) of dimension
+`dimension`.
 """
 struct Reals <: AbstractVectorSet
     dimension::Int
     function Reals(dimension::Base.Integer)
-        if !(dimension > 0)
+        if !(dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Reals must be > 0, not $(dimension).",
+                    "Dimension of Reals must be >= 0, not $(dimension).",
                 ),
             )
         end
@@ -130,15 +131,16 @@ dual_set_type(::Type{Reals}) = Zeros
 """
     Zeros(dimension)
 
-The set ``\\{ 0 \\}^{dimension}`` (containing only the origin) of dimension `dimension`.
+The set ``\\{ 0 \\}^{dimension}`` (containing only the origin) of dimension
+`dimension`.
 """
 struct Zeros <: AbstractVectorSet
     dimension::Int
     function Zeros(dimension::Base.Integer)
-        if !(dimension > 0)
+        if !(dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Zeros must be > 0, not $(dimension).",
+                    "Dimension of Zeros must be >= 0, not $(dimension).",
                 ),
             )
         end
@@ -152,15 +154,16 @@ dual_set_type(::Type{Zeros}) = Reals
 """
     Nonnegatives(dimension)
 
-The nonnegative orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\ge 0 \\}`` of dimension `dimension`.
+The nonnegative orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\ge 0 \\}`` of
+dimension `dimension`.
 """
 struct Nonnegatives <: AbstractVectorSet
     dimension::Int
     function Nonnegatives(dimension::Base.Integer)
-        if !(dimension > 0)
+        if !(dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Nonnegatives must be > 0, not $(dimension).",
+                    "Dimension of Nonnegatives must be >= 0, not $(dimension).",
                 ),
             )
         end
@@ -174,15 +177,16 @@ dual_set_type(::Type{Nonnegatives}) = Nonnegatives
 """
     Nonpositives(dimension)
 
-The nonpositive orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\le 0 \\}`` of dimension `dimension`.
+The nonpositive orthant ``\\{ x \\in \\mathbb{R}^{dimension} : x \\le 0 \\}`` of
+dimension `dimension`.
 """
 struct Nonpositives <: AbstractVectorSet
     dimension::Int
     function Nonpositives(dimension::Base.Integer)
-        if !(dimension > 0)
+        if !(dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of Nonpositives must be > 0, not $(dimension).",
+                    "Dimension of Nonpositives must be >= 0, not $(dimension).",
                 ),
             )
         end
@@ -274,7 +278,7 @@ struct NormInfinityCone <: AbstractVectorSet
         if !(dimension >= 1)
             throw(
                 DimensionMismatch(
-                    "Dimension of NormInfinityCone must be >= 1, not" *
+                    "Dimension of NormInfinityCone must be >= 1, not " *
                     "$(dimension).",
                 ),
             )
@@ -357,20 +361,23 @@ dual_set_type(::Type{RotatedSecondOrderCone}) = RotatedSecondOrderCone
 """
     GeometricMeanCone(dimension)
 
-The geometric mean cone ``\\{ (t,x) \\in \\mathbb{R}^{n+1} : x \\ge 0, t \\le \\sqrt[n]{x_1 x_2 \\cdots x_n} \\}`` of dimension `dimension```{}=n+1``.
+The geometric mean cone
+``\\{ (t,x) \\in \\mathbb{R}^{n+1} : x \\ge 0, t \\le \\sqrt[n]{x_1 x_2 \\cdots x_n} \\}``,
+where `dimension = n + 1 >= 2`.
 
-### Duality note
+## Duality note
 
 The dual of the geometric mean cone is
-``\\{ (u, v) \\in \\mathbb{R}^{n+1} : u \\le 0, v \\ge 0, -u \\le n \\sqrt[n]{\\prod_i v_i} \\}`` of dimension `dimension```{}=n+1``.
+``\\{ (u, v) \\in \\mathbb{R}^{n+1} : u \\le 0, v \\ge 0, -u \\le n \\sqrt[n]{\\prod_i v_i} \\}``,
+where `dimension = n + 1 >= 2`.
 """
 struct GeometricMeanCone <: AbstractVectorSet
     dimension::Int
     function GeometricMeanCone(dimension::Base.Integer)
-        if !(dimension > 1)
+        if !(dimension >= 2)
             throw(
                 DimensionMismatch(
-                    "Dimension of GeometricMeanCone must be > 1, not " *
+                    "Dimension of GeometricMeanCone must be >= 2, not " *
                     "$(dimension).",
                 ),
             )
@@ -436,7 +443,9 @@ end
 """
     RelativeEntropyCone(dimension)
 
-The relative entropy cone ``\\{ (u, v, w) \\in \\mathbb{R}^{1+2n} : u \\ge \\sum_{i=1}^n w_i \\log (\\frac{w_i}{v_i}), v_i \\ge 0, w_i \\ge 0 \\}`` of dimension `dimension```{}=2n+1``.
+The relative entropy cone
+``\\{ (u, v, w) \\in \\mathbb{R}^{1+2n} : u \\ge \\sum_{i=1}^n w_i \\log(\\frac{w_i}{v_i}), v_i \\ge 0, w_i \\ge 0 \\}``,
+where `dimension = 2n + 1 >= 3`.
 
 ### Duality note
 
@@ -446,11 +455,11 @@ The dual of the relative entropy cone is
 struct RelativeEntropyCone <: AbstractVectorSet
     dimension::Int
     function RelativeEntropyCone(dimension::Base.Integer)
-        if !(dimension >= 3 && isodd(dimension))
+        if !(dimension >= 1 && isodd(dimension))
             throw(
                 DimensionMismatch(
                     "Dimension of RelativeEntropyCone must be an odd integer " *
-                    ">= 3, not $(dimension).",
+                    ">= 1, not $(dimension).",
                 ),
             )
         end
@@ -461,18 +470,23 @@ end
 """
     NormSpectralCone(row_dim, column_dim)
 
-The epigraph of the matrix spectral norm (maximum singular value function) ``\\{ (t, X) \\in \\mathbb{R}^{1 + row_dim \\times column_dim} : t \\ge \\sigma_1(X) \\}`` where ``\\sigma_i`` is the ``i``th singular value of the matrix ``X`` of row dimension `row_dim` and column dimension `column_dim`.
-The matrix X is vectorized by stacking the columns, matching the behavior of Julia's `vec` function.
+The epigraph of the matrix spectral norm (maximum singular value function)
+``\\{ (t, X) \\in \\mathbb{R}^{1 + row_dim \\times column_dim} : t \\ge \\sigma_1(X) \\}``,
+where ``\\sigma_i`` is the ``i``th singular value of the matrix ``X`` of row
+dimension `row_dim` and column dimension `column_dim`.
+
+The matrix X is vectorized by stacking the columns, matching the behavior of
+Julia's `vec` function.
 """
 struct NormSpectralCone <: AbstractVectorSet
     row_dim::Int
     column_dim::Int
     function NormSpectralCone(row_dim::Base.Integer, column_dim::Base.Integer)
-        if !(row_dim > 0 && column_dim > 0)
+        if !(row_dim >= 0 && column_dim >= 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of NormSpectralCone must be strictly " *
-                    "positive, not ($(row_dim), $(column_dim)).",
+                    "Dimensions of NormSpectralCone must be >= 0, not " *
+                    "($(row_dim), $(column_dim)).",
                 ),
             )
         end
@@ -486,18 +500,23 @@ dual_set_type(::Type{NormSpectralCone}) = NormNuclearCone
 """
     NormNuclearCone(row_dim, column_dim)
 
-The epigraph of the matrix nuclear norm (sum of singular values function) ``\\{ (t, X) \\in \\mathbb{R}^{1 + row_dim \\times column_dim} : t \\ge \\sum_i \\sigma_i(X) \\}`` where ``\\sigma_i`` is the ``i``th singular value of the matrix ``X`` of row dimension `row_dim` and column dimension `column_dim`.
-The matrix X is vectorized by stacking the columns, matching the behavior of Julia's `vec` function.
+The epigraph of the matrix nuclear norm (sum of singular values function)
+``\\{ (t, X) \\in \\mathbb{R}^{1 + row_dim \\times column_dim} : t \\ge \\sum_i \\sigma_i(X) \\}``,
+where ``\\sigma_i`` is the ``i``th singular value of the matrix ``X`` of row
+dimension `row_dim` and column dimension `column_dim`.
+
+The matrix X is vectorized by stacking the columns, matching the behavior of
+Julia's `vec` function.
 """
 struct NormNuclearCone <: AbstractVectorSet
     row_dim::Int
     column_dim::Int
     function NormNuclearCone(row_dim::Base.Integer, column_dim::Base.Integer)
-        if !(row_dim > 0 && column_dim > 0)
+        if !(row_dim >= 0 && column_dim >= 0)
             throw(
                 DimensionMismatch(
-                    "Dimension of NormNuclearCone must be strictly " *
-                    "positive, not ($(row_dim), $(column_dim)).",
+                    "Dimension of NormNuclearCone must be >= 0, not " *
+                    "($(row_dim), $(column_dim)).",
                 ),
             )
         end
@@ -681,18 +700,19 @@ end
     PositiveSemidefiniteConeTriangle(side_dimension) <: AbstractSymmetricMatrixSetTriangle
 
 The (vectorized) cone of symmetric positive semidefinite matrices, with
-`side_dimension` rows and columns. See
-[`AbstractSymmetricMatrixSetTriangle`](@ref) for more details on the vectorized
-form.
+`side_dimension` rows and columns.
+
+See [`AbstractSymmetricMatrixSetTriangle`](@ref) for more details on the
+vectorized form.
 """
 struct PositiveSemidefiniteConeTriangle <: AbstractSymmetricMatrixSetTriangle
     side_dimension::Int
     function PositiveSemidefiniteConeTriangle(side_dimension::Base.Integer)
-        if !(side_dimension > 0)
+        if !(side_dimension >= 0)
             throw(
                 DimensionMismatch(
                     "Side dimension of PositiveSemidefiniteConeTriangle must " *
-                    "be strictly positive, not $(side_dimension).",
+                    "be >= 0, not $(side_dimension).",
                 ),
             )
         end
@@ -708,13 +728,18 @@ end
 """
     PositiveSemidefiniteConeSquare(side_dimension) <: AbstractSymmetricMatrixSetSquare
 
-The cone of symmetric positive semidefinite matrices, with side length `side_dimension`.
- See [`AbstractSymmetricMatrixSetSquare`](@ref) for more details on the vectorized
-form.
+The cone of symmetric positive semidefinite matrices, with side length
+`side_dimension`.
+
+See [`AbstractSymmetricMatrixSetSquare`](@ref) for more details on the
+vectorized form.
+
+The entries of the matrix are given column by column (or equivalently, row by
+row).
 
-The entries of the matrix are given column by column (or equivalently, row by row).
 The matrix is both constrained to be symmetric and to be positive semidefinite.
-That is, if the functions in entries ``(i, j)`` and ``(j, i)`` are different, then a constraint will be added to make sure that the entries are equal.
+That is, if the functions in entries ``(i, j)`` and ``(j, i)`` are different,
+then a constraint will be added to make sure that the entries are equal.
 
 ### Examples
 
@@ -725,18 +750,21 @@ Constraining the matrix
   -z & 0\\\\
 \\end{bmatrix}
 ```
-to be symmetric positive semidefinite can be achieved by constraining the vector ``(1, -z, -y, 0)`` (or ``(1, -y, -z, 0)``)
-to belong to the `PositiveSemidefiniteConeSquare(2)`.
-It both constrains ``y = z`` and ``(1, -y, 0)`` (or ``(1, -z, 0)``) to be in `PositiveSemidefiniteConeTriangle(2)`.
+to be symmetric positive semidefinite can be achieved by constraining the vector
+``(1, -z, -y, 0)`` (or ``(1, -y, -z, 0)``) to belong to the
+`PositiveSemidefiniteConeSquare(2)`.
+
+It both constrains ``y = z`` and ``(1, -y, 0)`` (or ``(1, -z, 0)``) to be in
+`PositiveSemidefiniteConeTriangle(2)`.
 """
 struct PositiveSemidefiniteConeSquare <: AbstractSymmetricMatrixSetSquare
     side_dimension::Int
     function PositiveSemidefiniteConeSquare(side_dimension::Base.Integer)
-        if !(side_dimension > 0)
+        if !(side_dimension >= 0)
             throw(
                 DimensionMismatch(
                     "Side dimension of PositiveSemidefiniteConeSquare must " *
-                    "be strictly positive, not $(side_dimension).",
+                    "be >= 0, not $(side_dimension).",
                 ),
             )
         end
@@ -764,17 +792,22 @@ end
 """
     LogDetConeTriangle(side_dimension)
 
-The log-determinant cone ``\\{ (t, u, X) \\in \\mathbb{R}^{2 + d(d+1)/2} : t \\le u \\log(\\det(X/u)), u > 0 \\}`` where the matrix `X` is represented in the same symmetric packed format as in the `PositiveSemidefiniteConeTriangle`.
-The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its number of rows or columns.
+The log-determinant cone
+``\\{ (t, u, X) \\in \\mathbb{R}^{2 + d(d+1)/2} : t \\le u \\log(\\det(X/u)), u > 0 \\}``,
+where the matrix `X` is represented in the same symmetric packed format as in
+the `PositiveSemidefiniteConeTriangle`.
+
+The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
+number of rows or columns.
 """
 struct LogDetConeTriangle <: AbstractVectorSet
     side_dimension::Int
     function LogDetConeTriangle(side_dimension::Base.Integer)
-        if !(side_dimension > 0)
+        if !(side_dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Side dimension of LogDetConeTriangle must " *
-                    "be strictly positive, not $(side_dimension).",
+                    "Side dimension of LogDetConeTriangle must be >= 0, not " *
+                    "$(side_dimension).",
                 ),
             )
         end
@@ -789,18 +822,25 @@ end
 """
     LogDetConeSquare(side_dimension)
 
-The log-determinant cone ``\\{ (t, u, X) \\in \\mathbb{R}^{2 + d^2} : t \\le u \\log(\\det(X/u)), X \\text{ symmetric}, u > 0 \\}`` where the matrix `X` is represented in the same format as in the `PositiveSemidefiniteConeSquare`.
-Similarly to `PositiveSemidefiniteConeSquare`, constraints are added to ensures that `X` is symmetric.
-The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its number of rows or columns.
+The log-determinant cone
+``\\{ (t, u, X) \\in \\mathbb{R}^{2 + d^2} : t \\le u \\log(\\det(X/u)), X \\text{ symmetric}, u > 0 \\}``,
+where the matrix `X` is represented in the same format as in the
+[`PositiveSemidefiniteConeSquare`](@ref).
+
+Similarly to [`PositiveSemidefiniteConeSquare`](@ref), constraints are added to
+ensure that `X` is symmetric.
+
+The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
+number of rows or columns.
 """
 struct LogDetConeSquare <: AbstractVectorSet
     side_dimension::Int
     function LogDetConeSquare(side_dimension::Base.Integer)
-        if !(side_dimension > 0)
+        if !(side_dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Side dimension of LogDetConeSquare must " *
-                    "be strictly positive, not $(side_dimension).",
+                    "Side dimension of LogDetConeSquare must be >= 0, not " *
+                    "$(side_dimension).",
                 ),
             )
         end
@@ -813,17 +853,22 @@ dimension(s::LogDetConeSquare) = 2 + s.side_dimension^2
 """
     RootDetConeTriangle(side_dimension)
 
-The root-determinant cone ``\\{ (t, X) \\in \\mathbb{R}^{1 + d(d+1)/2} : t \\le \\det(X)^{1/d} \\}`` where the matrix `X` is represented in the same symmetric packed format as in the `PositiveSemidefiniteConeTriangle`.
-The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its number of rows or columns.
+The root-determinant cone
+``\\{ (t, X) \\in \\mathbb{R}^{1 + d(d+1)/2} : t \\le \\det(X)^{1/d} \\}``,
+where the matrix `X` is represented in the same symmetric packed format as in
+the [`PositiveSemidefiniteConeTriangle`](@ref).
+
+The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
+number of rows or columns.
 """
 struct RootDetConeTriangle <: AbstractVectorSet
     side_dimension::Int
     function RootDetConeTriangle(side_dimension::Base.Integer)
-        if !(side_dimension > 0)
+        if !(side_dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Side dimension of RootDetConeTriangle must " *
-                    "be strictly positive, not $(side_dimension).",
+                    "Side dimension of RootDetConeTriangle must be >= 0, not " *
+                    "$(side_dimension).",
                 ),
             )
         end
@@ -838,18 +883,25 @@ end
 """
     RootDetConeSquare(side_dimension)
 
-The root-determinant cone ``\\{ (t, X) \\in \\mathbb{R}^{1 + d^2} : t \\le \\det(X)^{1/d}, X \\text{ symmetric} \\}`` where the matrix `X` is represented in the same format as in the `PositiveSemidefiniteConeSquare`.
-Similarly to `PositiveSemidefiniteConeSquare`, constraints are added to ensure that `X` is symmetric.
-The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its number of rows or columns.
+The root-determinant cone
+``\\{ (t, X) \\in \\mathbb{R}^{1 + d^2} : t \\le \\det(X)^{1/d}, X \\text{ symmetric} \\}``,
+where the matrix `X` is represented in the same format as
+[`PositiveSemidefiniteConeSquare`](@ref).
+
+Similarly to [`PositiveSemidefiniteConeSquare`](@ref), constraints are added to
+ensure that `X` is symmetric.
+
+The argument `side_dimension` is the side dimension of the matrix `X`, i.e., its
+number of rows or columns.
 """
 struct RootDetConeSquare <: AbstractVectorSet
     side_dimension::Int
     function RootDetConeSquare(side_dimension::Base.Integer)
-        if !(side_dimension > 0)
+        if !(side_dimension >= 0)
             throw(
                 DimensionMismatch(
-                    "Side dimension of RootDetConeSquare must " *
-                    "be strictly positive, not $(side_dimension).",
+                    "Side dimension of RootDetConeSquare must be >= 0, not " *
+                    "$(side_dimension).",
                 ),
             )
         end
@@ -1046,7 +1098,7 @@ defines the complementarity problem where `0 <= x_1 ⟂ x_3 >= 0` and
 struct Complements <: AbstractVectorSet
     dimension::Int
     function Complements(dimension::Base.Integer)
-        if !(dimension > 0 && iseven(dimension))
+        if !(dimension >= 0 && iseven(dimension))
             throw(
                 DimensionMismatch(
                     "Dimension of Complements must be even, not $(dimension).",
diff --git a/test/sets.jl b/test/sets.jl
index e98d3e697c..6054bc79fe 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -115,28 +115,37 @@ function test_sets_dimension()
 end
 
 function test_sets_DimensionMismatch()
-    @test_throws DimensionMismatch MOI.Reals(0)
-    @test_throws DimensionMismatch MOI.Zeros(0)
-    @test_throws DimensionMismatch MOI.Nonnegatives(0)
-    @test_throws DimensionMismatch MOI.Nonpositives(0)
-    @test_throws DimensionMismatch MOI.NormInfinityCone(0)
-    @test_throws DimensionMismatch MOI.NormOneCone(0)
-    @test_throws DimensionMismatch MOI.SecondOrderCone(0)
-    @test_throws DimensionMismatch MOI.RotatedSecondOrderCone(1)
-    @test_throws DimensionMismatch MOI.GeometricMeanCone(1)
-    @test_throws DimensionMismatch MOI.RelativeEntropyCone(1)
-    @test_throws DimensionMismatch MOI.RelativeEntropyCone(4)
-    @test_throws DimensionMismatch MOI.NormSpectralCone(1, 0)
-    @test_throws DimensionMismatch MOI.NormSpectralCone(0, 1)
-    @test_throws DimensionMismatch MOI.NormNuclearCone(1, 0)
-    @test_throws DimensionMismatch MOI.NormNuclearCone(0, 1)
-    @test_throws DimensionMismatch MOI.PositiveSemidefiniteConeTriangle(0)
-    @test_throws DimensionMismatch MOI.PositiveSemidefiniteConeSquare(0)
-    @test_throws DimensionMismatch MOI.LogDetConeTriangle(0)
-    @test_throws DimensionMismatch MOI.LogDetConeSquare(0)
-    @test_throws DimensionMismatch MOI.RootDetConeTriangle(0)
-    @test_throws DimensionMismatch MOI.RootDetConeSquare(0)
-    @test_throws DimensionMismatch MOI.Complements(0)
+    for (S, min_dimension) in (
+        (MOI.Reals, 0),
+        (MOI.Zeros, 0),
+        (MOI.Nonnegatives, 0),
+        (MOI.Nonpositives, 0),
+        (MOI.NormInfinityCone, 1),
+        (MOI.NormOneCone, 1),
+        (MOI.SecondOrderCone, 1),
+        (MOI.RotatedSecondOrderCone, 2),
+        (MOI.GeometricMeanCone, 2),
+        (MOI.Complements, 0),
+        (MOI.RelativeEntropyCone, 1),
+        (MOI.PositiveSemidefiniteConeTriangle, 0),
+        (MOI.PositiveSemidefiniteConeSquare, 0),
+        (MOI.LogDetConeTriangle, 0),
+        (MOI.LogDetConeSquare, 0),
+        (MOI.RootDetConeTriangle, 0),
+        (MOI.RootDetConeSquare, 0),
+    )
+        @test_throws DimensionMismatch S(min_dimension-1)
+        @test S(min_dimension) isa S
+    end
+    @test_throws DimensionMismatch MOI.NormSpectralCone(-1, 0)
+    @test_throws DimensionMismatch MOI.NormSpectralCone(0, -1)
+    @test MOI.NormSpectralCone(0, 0) isa MOI.NormSpectralCone
+    @test_throws DimensionMismatch MOI.NormNuclearCone(-1, 0)
+    @test_throws DimensionMismatch MOI.NormNuclearCone(0, -1)
+    @test MOI.NormNuclearCone(0, 0) isa MOI.NormNuclearCone
+    # Other dimension checks
+    @test_throws DimensionMismatch MOI.RelativeEntropyCone(2)
+    @test_throws DimensionMismatch MOI.Complements(-3)
     @test_throws DimensionMismatch MOI.Complements(3)
     return
 end

From 326f1e638971d394a71b20df7d83d9084e882295 Mon Sep 17 00:00:00 2001
From: Oscar Dowson <odow@users.noreply.github.com>
Date: Mon, 7 Jun 2021 15:40:54 +1200
Subject: [PATCH 10/14] Update sets.jl

---
 test/sets.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/sets.jl b/test/sets.jl
index 6054bc79fe..7f8fcab254 100644
--- a/test/sets.jl
+++ b/test/sets.jl
@@ -134,7 +134,7 @@ function test_sets_DimensionMismatch()
         (MOI.RootDetConeTriangle, 0),
         (MOI.RootDetConeSquare, 0),
     )
-        @test_throws DimensionMismatch S(min_dimension-1)
+        @test_throws DimensionMismatch S(min_dimension - 1)
         @test S(min_dimension) isa S
     end
     @test_throws DimensionMismatch MOI.NormSpectralCone(-1, 0)

From 7efd7d94824464de9129dee2d4a143562124fa37 Mon Sep 17 00:00:00 2001
From: Oscar Dowson <odow@users.noreply.github.com>
Date: Fri, 18 Jun 2021 14:45:51 +1200
Subject: [PATCH 11/14] Update SDPA.jl

---
 src/FileFormats/SDPA/SDPA.jl | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/src/FileFormats/SDPA/SDPA.jl b/src/FileFormats/SDPA/SDPA.jl
index 079a538ec6..5fa9e8d971 100644
--- a/src/FileFormats/SDPA/SDPA.jl
+++ b/src/FileFormats/SDPA/SDPA.jl
@@ -164,11 +164,8 @@ function Base.write(io::IO, model::Model{T}) where {T}
     end
     println(io)
 
-    max_index_dim = if max_dim > 0
+    max_index_dim =
         MOI.dimension(MOI.PositiveSemidefiniteConeTriangle(max_dim))
-    else
-        0
-    end
     index_map = Vector{Tuple{Int,Int}}(undef, max_index_dim)
     k = 0
     for col in 1:max_dim

From db0c1962b31c0f7769e68d6748fdb997c1345a27 Mon Sep 17 00:00:00 2001
From: Oscar Dowson <odow@users.noreply.github.com>
Date: Fri, 18 Jun 2021 14:46:25 +1200
Subject: [PATCH 12/14] Update map.jl

---
 test/Bridges/Variable/map.jl | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/test/Bridges/Variable/map.jl b/test/Bridges/Variable/map.jl
index bf3de204ef..7dcc31172e 100644
--- a/test/Bridges/Variable/map.jl
+++ b/test/Bridges/Variable/map.jl
@@ -86,11 +86,8 @@ v2, c2 = MOIB.Variable.add_keys_for_bridge(map, () -> b2, set2)
     @test collect(values(map)) == [b1, b2]
 end
 
-struct _ZeroDimSet <: MOI.AbstractVectorSet
-    dimension::Int
-end
 b3 = VariableDummyBridge(3)
-set3 = _ZeroDimSet(0)
+set3 = MOI.Zeros(0)
 v3, c3 = MOIB.Variable.add_keys_for_bridge(map, () -> b3, set3)
 @testset "Vector set of length 0" begin
     @test isempty(v3)

From 58430a0fab80c9461ff7692830630489f94ee24e Mon Sep 17 00:00:00 2001
From: Oscar Dowson <odow@users.noreply.github.com>
Date: Fri, 18 Jun 2021 14:48:02 +1200
Subject: [PATCH 13/14] Update sets.jl

---
 src/sets.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/sets.jl b/src/sets.jl
index 1c818858ce..88564ec3d8 100644
--- a/src/sets.jl
+++ b/src/sets.jl
@@ -445,7 +445,7 @@ end
 
 The relative entropy cone
 ``\\{ (u, v, w) \\in \\mathbb{R}^{1+2n} : u \\ge \\sum_{i=1}^n w_i \\log(\\frac{w_i}{v_i}), v_i \\ge 0, w_i \\ge 0 \\}``,
-where `dimension = 2n + 1 >= 3`.
+where `dimension = 2n + 1 >= 1`.
 
 ### Duality note
 

From 0e6076a9047d007a4927c20009a076befec60905 Mon Sep 17 00:00:00 2001
From: Oscar Dowson <odow@users.noreply.github.com>
Date: Mon, 21 Jun 2021 09:14:00 +1200
Subject: [PATCH 14/14] Update SDPA.jl

---
 src/FileFormats/SDPA/SDPA.jl | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/src/FileFormats/SDPA/SDPA.jl b/src/FileFormats/SDPA/SDPA.jl
index 5fa9e8d971..a85e75cfb6 100644
--- a/src/FileFormats/SDPA/SDPA.jl
+++ b/src/FileFormats/SDPA/SDPA.jl
@@ -164,8 +164,7 @@ function Base.write(io::IO, model::Model{T}) where {T}
     end
     println(io)
 
-    max_index_dim =
-        MOI.dimension(MOI.PositiveSemidefiniteConeTriangle(max_dim))
+    max_index_dim = MOI.dimension(MOI.PositiveSemidefiniteConeTriangle(max_dim))
     index_map = Vector{Tuple{Int,Int}}(undef, max_index_dim)
     k = 0
     for col in 1:max_dim